% Mizar problem: t38_rewrite1,rewrite1,801,31 
fof(t38_rewrite1,conjecture,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( ( r5_rewrite1(A,B,C)
            | r6_rewrite1(A,B,C) )
         => r2_rewrite1(A,B,C) ) ) ),
    inference(mizar_bg_added,[status(thm)],[d7_rewrite1,d8_rewrite1,t26_rewrite1,t31_rewrite1]),
    [file(rewrite1,t38_rewrite1)]).

fof(d7_rewrite1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( r5_rewrite1(A,B,C)
        <=> ? [D] : 
              ( r1_rewrite1(A,B,D)
              & r1_rewrite1(A,C,D) ) ) ) ),
    file(rewrite1,d7_rewrite1),
    []).

fof(d8_rewrite1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( r6_rewrite1(A,B,C)
        <=> ? [D] : 
              ( r1_rewrite1(A,D,B)
              & r1_rewrite1(A,D,C) ) ) ) ),
    file(rewrite1,d8_rewrite1),
    []).

fof(t26_rewrite1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( r1_rewrite1(A,B,C)
         => ( r2_rewrite1(A,B,C)
            & r2_rewrite1(A,C,B) ) ) ) ),
    file(rewrite1,t26_rewrite1),
    []).

fof(t31_rewrite1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C,D] : 
          ( ( r2_rewrite1(A,B,C)
            & r2_rewrite1(A,C,D) )
         => r2_rewrite1(A,B,D) ) ) ),
    file(rewrite1,t31_rewrite1),
    []).